In this review, a new classification of elements based on behavior in hydrofluoric acid (HF) solution is presented for the precise quantitative analysis of each element by inductively coupled plasma mass spectrometry (ICP-MS). The elements are divided into 7 groups: (1) "fluorophile" elements; (2) insoluble fluoride-forming elements; (3) "bromophile" or "iodophile" elements; (4) "oxophile" elements; (5) "aquaphile" elements; (6) bare cation elements; and (7) other elements. Especially, the importance of fluorophile and insoluble fluoride-forming elements in elemental analysis is described. Due to the elemental characteristics, these two groups of elements cannot be dissolved simultaneously in the same solution, and thus cannot be measured together. In addition, coprecipitation of the fluorophile elements with the insoluble fluorides occurs in some conditions and hinders accurate analysis. The peculiar conditions when the coprecipitation occurs are discussed, and the "Al-addition" and "Mg-addition" methods for overcoming these problems are described. In addition, some state-of-the-art analytical techniques in ICP-MS are shown, and future directions of the element analysis are presented.